The coefficient of x 4 in x -2-3- x 210 isA- 450 - 263B- NoneC- 504 - 259D- 405 - 256

The correct option is D 405/256 T_r+1 = ^10C_r (x/2)^10 r( 3/x^2)^r Equating power of x to 4 10 3r = 4 ⇒ r = 2 So coefficient of x^4 is ^10C_2 (1/2)^8 ( 3)^2 ...

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Standard XII

Mathematics

Combination

The coefficie...

Question

The coefficient of $x^{4}$ in ${(\frac{x}{2} - \frac{3}{x^{2}})}^{10}$ is:

405/256

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504/259

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450/263

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None

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Solution

The correct option is A
405/256

$T_{r + 1} =^{10} C_{r} {(\frac{x}{2})}^{10 - r} {(- \frac{3}{x^{2}})}^{r}$

Equating power of x to 4

10 - 3r = 4 $\Rightarrow$ r = 2

So coefficient of $x^{4}$ is $^{10} C_{2} {(\frac{1}{2})}^{8} (- 3)^{2}$

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Similar questions

Q. The coefficient of

x^{4}

in the expansion of

{(\frac{x}{2} - \frac{3}{x^{2}})}^{10}

Q. Coefficient of

x^{4}

(\frac{x}{2} - \frac{3}{x^{2}})^{10}

Q. The coefficient of

x^{4}

{(\frac{x}{2} - \frac{3}{x^{2}})}^{10}

Q. In the expansion of

{(\frac{x}{2} - \frac{3}{x^{2}})}^{10}

, the coefficient of

x^{4}

Q. Find the coefficient of

x^{4}

in the expansion of

{(x / 2 - {3 / x}^{2})}^{10}

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The coefficient of x4 in (x2−3x2)10 is:

The correct option is A 405/256 Tr+1=10Cr(x2)10−r(−3x2)r Equating power of x to 4 10 - 3r = 4 ⇒ r = 2 So coefficient of x4 is 10C2(12)8(−3)2

The coefficient of $x^{4}$ in ${(\frac{x}{2} - \frac{3}{x^{2}})}^{10}$ is:

The correct option is A
405/256

$T_{r + 1} =^{10} C_{r} {(\frac{x}{2})}^{10 - r} {(- \frac{3}{x^{2}})}^{r}$

Equating power of x to 4

10 - 3r = 4 $\Rightarrow$ r = 2

So coefficient of $x^{4}$ is $^{10} C_{2} {(\frac{1}{2})}^{8} (- 3)^{2}$